Redirecting X over tcp / udp and using something like "XWin -query machine" is insecure. So are most VNC solutions. You can use X forwarding over ssh:
% ssh -X -C -c blowfish MachineHostname xterm
(Blowfish encryption tends to be a bit faster, and -C enforces compression, though it should be enabled by default. If you have issues with X forwarding, check your /etc/ssh/sshd_config for "X11Forwarding yes" and "ForwardX11 yes").
Sometimes you _have_ to run a graphical interface on a UNIX machine, and do so from your Windows box. Examples include the Oracle Installer and some other Java applications.
While you could install Cygwin to provide you with an XOrg server implementation, Cygwin tends to be quite big. A lighter and faster option would be to use XMing. It's small, fast and just works. Just fire up XWin, and it will listen on 0:0 by default.
Now you can use "ssh -X machineIP xterm" and it will start a remote XTerm right on your machine. Or if you use putty, make sure you redirect X:
Now run your favorite GUI application.